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a. Show that there is no solution to the boundary value problem$$y^{\prime \prime}+4 y=0, \quad y(0)=0, y(\pi)=1$$b. Show that there are infinitely many solutions to the boundary value problem$$y^{\prime \prime}+4 y=0, \quad y(0)=0, y(\pi)=0$$

Calculus 3

Chapter 17

Second-Order Differential Equations

Section 1

Second-Order Linear Equations

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a. Show that there is no s…

For part a we have 4 minus y double prime. We 4 times we have y double prime plus 1 pi, which is equal to 0. With y 0 equaling, 0 n y coinaurpot, 0 r is equal pumistone. I y t is equal to c 1 cosine, 2 t plus c 292 t pot, so y of 0 is supposed to be equal to c 1 equal to 0 c 1 is 0, and if that's the case, why pie is the loop in times is supposed To be is not equal to or equal to 1 and sine sine of 2 piglead for part b we have y double fine plus 4 times y equals 0 on y 0 equals 0, and i i equaling so this is r squared plus 4 times plus 4 Equals 0, so then y t equals c 1 cosine t, k, plus z, t sin. J g, hi, equal p 1, which is 0 so y t, is equal. Tuctoo, which is equal to 0, is equal to something y of pi, meaning c 2 times si or 2 to 2. Pi is equal to 0, so c 2 could be any value. Tents, pi equals 0.

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